This research involves creating, exploring and testing mathematical models of dendritic neurons that are relevant to experimental neurophysiology and neuroanatomy. Together these models provide a theory that can account for various sequences of events in the soma and dendritic branches of a single neuron, and for field potentials generated by certain cortical populations of neurons. Computational experiments performed with these models provide theoretical predictions that have been compared with experimental results obtained by colleagues with motoneurons of cat spinal cord, and with the mitral cell and granule cell populations of rabbit olfactory bulb. Resulting interpretations contribute to understanding of dendritic synaptic input and of dendro-dendritic synaptic interactions. Several important consequences of assuming excitable membrane properties at the heads of dendritic spines have been explored computationally and presented at symposia. For distal dendritic locations, the firing of one (or a few) excitable spines may trigger (through spread of sufficient depolarization along the dendritic shaft) the firing of neighboring excitable spines. Such a chain-reaction will usually spread (and fire) only a subset of the available excitable spine clusters. Whether a spine cluster fires or not depends (with nonlinear sensitivity) upon changes in synaptic excitation and inhibition and changes in spine stem resistance or other spine parameters. The thousands of spines and synaptic contacts per neuron can provide a rich repertoire of logical operaitons implemented by excitable spine clusters; explicit examples are being explored. The collaboration of Holmes and Woody extends similar neural modeling and testing to include complications resulting from non-uniform Rm and non-uniform synaptic background activitiy in pyramidal cells of cerebral cortex; explicit examples are being explored.